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So a 2,000-square-foot crawl space would need a 40 cfm exhaust fan. It's pulling just a little bit of air from the crawl space. The problem is that you don't really know where the makeup air for the crawl space is coming from. Yes, the code specifies a pathway for air to move into the crawl space from the house, but air doesn't always follow those arrows in the diagrams.
Automatic vents are less fuss. Air Vent makes ones that open at about 70 degrees F, close about 40, and don't require any electricity. You do not say whether your crawl- space floor is made of dirt or concrete, but if it is dirt, spread 6-millimeter plastic sheeting over it to help block that source of moisture.